How do you calculate the molarity of the soln?

This one's pretty tricky... (You're NOT stupid.)

Let's start with some relevant definitions:
A solution comprises a solute, the thing being dissolved, and a solvent, the thing doing the dissolving.

mole fraction = (moles of solute) / (moles solution) [1]

molarity = (moles of solute) / (liters of solution) [2]

For this conversion, let's use 1 mole of solution to make the calculation easier and the concepts a bit more clear (though it really doesn't matter how much we use).
From [1]:
0.0194 = (moles of solute) / 1
moles of solute = 0.0194

moles of solution = (moles of solute) + (moles of solvent)
1 = 0.0194 + (moles of solvent)
moles of solvent = 0.9806

The only thing given in the problem to help us with converting to "liters of solution" is the density of the solution (in g/ml). We'll first have to convert the moles of solute and moles of solvent to grams in order to use the density for conversion to liters:
g solute = (moles of solute)(molar mass of solute KNO3)

molar mass of KNO3 = 39.098 + 14.007 + 3*15.999 g/mol = 101.102 g/mol

g solute = (0.0194 mol)(101.102 g/mol) = 1.96 g
---

g solvent = (moles of solvent)(molar mass of solvent H2O)

molar mass of H2O = 2*1.0079 + 15.999 g/mol = 18.0148 g/mol

g solvent = (0.9806 mol)(18.0148 g/mol) = 17.67 g
---

g solution = (g of solute) + (g of solvent)
g solution = 1.96 + 17.67 g = 19.63 g

Now we can convert g solution into L of solution:
(19.63 g)(ml / 1.0627 g)(L / 1000 ml) = 0.01847 L

From [2]:
molarity = (0.0194 mol) / (0.01847 L) = 1.05 M